Brenda is going from $(-4,5)$ to $(5,-4)$, but she needs to stop by the origin on the way. How far does she have to travel?
Answers
Answer:
2[tex]\sqrt{41}[/tex] units is the distance that Brenda is going to travel.
Step-by-step explanation:
Given that:
Brenda starts from point [tex](-4,5)[/tex] to [tex](5,-4)[/tex]
Let point P [tex](-4,5)[/tex] and Q [tex](5,-4)[/tex].
But given that she need to stop by origin O[tex](0, 0)[/tex].
So, she travels from P to O first and then goes form O to Q.
Please refer to the attached figure for better understanding.
We need to find the distance PO + OQ to find the total distance traveled by Brenda.
We can use Distance formula :
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For PO:
[tex]x_2 = 0\\x_1 = -4\\y_2 = 0\\y_1 = 5[/tex]
[tex]PO = \sqrt{(0-(-4))^2+(0-5)^2}\\\Rightarrow PO = \sqrt{(4)^2+(5)^2} = \sqrt{41}\ units[/tex]
Similarly, For OQ:
[tex]x_2 = 5\\x_1 = 0\\y_2 = -4\\y_1 =0[/tex]
[tex]OQ = \sqrt{(5-0)^2+(-4-0)^2}\\\Rightarrow OQ = \sqrt{(5)^2+(4)^2} = \sqrt{41}\ units[/tex]
So, the total distance traveled = PO + OQ = [tex]\sqrt{41}+\sqrt{41}=2\sqrt{41}\ units[/tex]
2[tex]\sqrt{41}[/tex] units is the distance that Brenda is going to travel.
Related Questions
There are members on the board of directors for a certain non-profit institution. a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? b. If they must form an ethics subcommittee of four members, how many different subcommittees are possible?
Answers
Answer: a. 1320
b.495
Step-by-step explanation:
Complete question is provided in the attachment.
Total members on the board = 12
a. Persons to chose : chairperson, first vice chairperson, second vice chairperson, and secretary
i.e. Total 3 posts in an order.
Number of ways to choose 3 persons from 12 in an order = [tex]^{12}P_3[/tex] [By permutation]
[tex]=\dfrac{12!}{(12-3)!}\\\\=\dfrac{12!}{7!}\\\\=12\times11\times10\\\\=1320[/tex]
hence, 1320 different slates of candidates are possible .
b. number of ways to choose 4 members out of 12 ( order not matters)=[tex]^{12}C_{4}[/tex] [By combinations]
[tex]=\dfrac{12!}{4!8!}\\\\=\dfrac{12\times11\times10\times9}{24}\\\\=495[/tex]
Hence, the number of different subcommittees are possible =495
I need help in this page
Answers
Step-by-step explanation:
a. 3.14 * 4² = 50.24 cm²
b. 16 cm
c. V = B * h = 50.24 * 16 = 803.84 cm²
A. 50.24
B. 16
C. 50.24 , 16 ,803.84
Explain
A. Area = πr^2 = 3.14(4)^2= 50.24
B. Volume = area x height = 50.24 x 16 = 803 . 84 cubic cm
So for part c the answer are 50.24 , 16 , 803.84
Hopefully this help you :D
In the figure, a//b, and both lines are intersected by transversal t. Complete the statements to prove that m<1=m<5.
Answers
Answer:
Transitive Property of EqualityAlternate Interior Angles TheoremStep-by-step explanation:
a) You're trying to justify that two sums equal to 180° are equal to each other. The Transitive Property of Equality is that justification.
__
b) You're trying to justify that angles 3 and 6 are congruent. These are between the parallel lines, so are "interior" angles. They are on opposite sides of the transversal, so are "alternate" angles. They do not share a vertex, so cannot be vertical angles. The applicable theorem is the Alternate Interior Angles Theorem.
Answer:
Step-by-step explanation:
A pallet of floor tiles contains 40 cases of tiles and the yard has 10 complete pallets of tile. If you remove 180 cases for one customer how many cases of tiles will be remaining in the yard? *
Answers
Answer:
220 cases
Step-by-step explanation:
Each pallet contains 40 cases of tiles.
The yard has 10 complete pallets.
The total number of cases of tiles is therefore:
40 * 10 = 400 cases
If 180 cases are removed for the customer, then the number of cases of tiles remaining is:
400 - 180 = 220 cases
220 cases of tiles will be remaining.
Tom takes a cancer test and the test is advertised as being 99% accurate: if you have cancer you will test positive 99% of the time, and if you don't have cancer, you will test negative 99% of the time. If 1% of all people have cancer and Tom tests positive, what is the prob that Tom has the disease
Answers
Answer:
99% chance tommy has it
Step-by-step explanation:
cuz do da math
Sketch the graph of the inequality. 3y − x ≥ 9
Answers
Answer:
The graph of inequality is shown below.
Step-by-step explanation:
The given inequality is
[tex]3y-x\geq 9[/tex]
Related equation is
[tex]3y-x=9[/tex]
At x=0,
[tex]3y-0=9\Rightarrow y=3[/tex]
At y=0,
[tex]3(0)-x=9\Rightarrow x=-9[/tex]
Plot (0,3) and (-9,0) on coordinate plane and connect them by a straight line.
Check the inequality for (0,0).
[tex]3(0)-(0)\geq 9[/tex]
[tex]0\geq 9[/tex]
This statement is false. So, (0,0) is not included in the shaded region.
The graph of inequality is shown below.
The table represents an exponential function.
What is the multiplicative rate of change of the
function?
x
1
0 1 / 3
2
3
0 2 3
y
6
4
8
3
16
9
O 2
09
4.
Answers
Question Correction
The table represents an exponential function. What is the multiplicative rate of change of the function?
(A)1/3 (B)2/3 (C)2 (D)9
[tex]\left|\begin{array}{c|c}x&y\\--&--\\1&9\\2&6\\3&4\\4&\dfrac83\\\\5&\dfrac{16}{9}\end{array}\right|[/tex]
Answer:
(B) [tex]\dfrac{2}{3}[/tex]
Step-by-step explanation:
An exponential function is a function of the form
[tex]y= a (b)^{x}[/tex]
where a is the initial value and b is the multiplicative rate of change
When x=2, y=6, we have:
[tex]6= a (b)^{2}[/tex]
When x=3, y=4, we have:
[tex]4= a (b)^{3}[/tex]
Dividing the two equations:
[tex]\dfrac{a (b)^{3}}{a (b)^{2}} =\dfrac{6}{9} \\b=\dfrac{6}{9}\\b=\dfrac{2}{3}[/tex]
The multiplicative rate of change, b is [tex]\dfrac{2}{3}[/tex].
The correct option is B.
Answer: It's B) 2/3
Hope it helps :3
which of the following descriptions represent the transformation shown in the image? Part 3c
Answers
Answer: c) rotation of 180° & shift right 1 unit and down 2 units
Step-by-step explanation:
Rotation of 180° changes the signs of x and y
(x, y) → (-x, -y)
Shift right one unit adds 1 to x, Shift two down subtracts 2 from y
(-x, -y) → (-x + 1, -y - 2)
(x, y) (-x + 1, -y - 2)
(-1, -2) → (2, 0)
(-4, -1) → (5, -1)
(-4, -3) → (5, 1)
The organization that Jones works for is running for a father son dinner for those employees is invited to attend along with his youngest son. If Jones is known to have two children, what is the condition probability that they are both boys given that he is invited to the dinner?
Answers
Answer:
25%
Step-by-step explanation:
The probability of having a boy is 50%
To calculate the probability of him having 2 boys, multiply the probabilities together
0.5(0.5) = 0.25
The marketing research department of a computer company used a large city to test market the firm's new laptop. The department found the relationship between price p (dollars per unit) and the demand x (units per week) was given approximately by the following equation.
p= 1275 = 0.17x^2 0 < x < 80
So, weekly revenue can be approximated by the following equation.
R(x)= rp = 1275x- 0.17x^3 0 < x <80
Required:
a. Find the local extrema for the revenue function. What is/are the local maximum/a?
b. On which intervals is the graph of the revenue function concave upward?
c. On which intervals is the graph of the revenue function concave downward?
Answers
Answer:
a. Local maximum = 50 units per week.
b. The graph is never concave upward.
c. (0, 80)
Step-by-step explanation:
a. The revenue function is:
[tex]R(x) = 1275x-0.17x^3[/tex]
The derivate of the revenue function for which R'(x) = 0 gives us the local extrema:
[tex]R'(x) =0= 1275-0.51x^2\\x=\sqrt{2,500}\\x=50[/tex]
The second derivate of the revenue function determines if x =50 is local maximum or minimum:
[tex]R''(x) = -1.02x\\R''(50) = -1.02*50=-51\\[/tex]
Since the second derivate yields a negative value, x = 50 units per week is a local maximum.
b. Since there are no local minimums in the range of 0 < x < 80, the graph is never concave upward.
c. Since there is only one local maximum in the range of 0 < x < 80, the graph is concave downward from x>0 to x<80 or (0, 80)
Write 6 17/20 as a decimal
Answers
Answer:
6.85
Step-by-step explanation:
6 17/20
Convert to improper fraction.
137/20
Divide.
= 6.85
Answer:
6.85
Step-by-step explanation:
17/20 = 85/100
17 x 5 = 85
20 x 5 = 100
so,
6 + 85/100 = 6.85
simplify the expression into form a+bi, where rational numbers
(4-i)(-3+7i) - 7i(8+2i)
Answers
Answer:
-12+28i+3i-7i-65i+28
14 -41i
T or F? Is 3y=5x If x is 3 and y is 5?
Answers
Answer:
True
Step-by-step explanation:
3y=5x
Put x as 3 and y as 5.
3(5) = 5(3)
15 = 15
Hence, true.
Answer:
trueX=3
y=15
[tex]3y = 5x \\ 3 \times 5 = 5 \times 3 \\ 15 = 15[/tex]
Proved.
Hope it helps..
will give brainliest help plz i can't get back on the password won't go to my email and my little brother changed the password I am scared I lost everything PLZ HELP ME
Answers
-5 x = 4 what property of equality was use to solve this equation
Answers
Answer:
Division property of equality.
5x is equal to 8X raise to power - 1/3
Answers
Answer:
No solutions.
Step-by-step explanation:
5x = 8x^-1/3
Divide 8 into both sides.
5/8x = x^-1/3
Divide both sides by x.
5/8 = x^-4/3
Multiply both sides by the exponent -3/4.
5/8^-3/4 = x
1.422624 = x
Plug in 1.422624 for x to check.
It does not work. There are no real solutions.
Which parent function is f(x) = x^2?
O A. An exponential parent function
OB. The linear parent function
C. The absolute value parent function
D. The quadratic parent function
Answers
Answer:
D. Quadratic parent function.
Step-by-step explanation:
What is the measure of angle ABC? Please answer quickly!
Answers
Answer:
ABC = 88
Step-by-step explanation:
Angle Formed by Two Chords = 1/2( sum of Intercepted Arcs)
ABD = 1/2 ( 131+ 53)
ABD = 1/2 (184)
=92
ABC = 180 -ABD
ABC = 88
Need Help!!!! What is 1495486+73940426 Thanks!
Answers
Answer:
75435912
Step-by-step explanation:
1495486+73940426
= 75435912
Answer:
75,435,912
Step-by-step explanation:
=> 1495486 + 73940426
Using Calculator
=> 75,435,912
A student earned grades of B, B, A, C, and D. Those courses had these corresponding numbers of credit hours: 4, 5, 1, 5, 4. The grading system assigns quality points to letter grades as follows: Aequals=4, Bequals=3, Cequals=2, Dequals=1, and Fequals=0. Compute the grade point average (GPA) and round the result to two decimal places.
Answers
Answer:
1.69Step-by-step explanation:
Let the five courses with their corresponding credit hours be represented as shown;
FST 201 = 4
FST 203 = 5
FST 112 = 1
FST 219 = 5
FST 223 = 4
If a student earned grades of B, B, A, C, and D respectively in those courses with the following grading system A =4, B =3, C =2, D =1, and F =0, before we can get the student GPA, we need to know the total credit point for the five courses.
Credit point for each course = Number of credit hour * point for each grade
FST 201 = 4 * 4 = 16points (A)
FST 203 = 5 * 4 = 20points (A)
FST 112 = 1 * 4 = 4points (A)
FST 219 = 5 * 4 = 20points (A)
FST 223 = 4 * 4 = 16points (A)
Total credit point = 16+20+4+20+16 = 76points
Total credit point gotten by the student is calculated as thus;
FST 201 = 4 * 3 = 12points (B)
FST 203 = 5 * 3 = 15points (B)
FST 112 = 1 * 4 = 4points (A)
FST 219 = 5 * 2 = 10points (C)
FST 223 = 4 * 1 = 4points (D)
Total credit point gotten by the student = 45points.
student's Grade Point Average (GPA) = Total credit point/Total credit point gotten by the student = 76/45 = 1.69 (to 2dp)
4) →BRAINLIEST & 10+ POINTS! ← A wheel with diameter 44 cm completes four revolutions in 0.5 seconds. Find the linear speed of the edge of the wheel in cm per second. ⇒Round to the nearest whole number. Linear speed = ____ cm/s
Answers
Answer:
352 cm/s
Step-by-step explanation:
circ = 44pi
speed = distance * time
distance = circ * 4 = 176pi
speed = 176pi/0.5
Answer:
≈ 1106 cm/s
Step-by-step explanation:
linear speed = angular speed x radius of the rotation
v = ωr
v = linear speed (m/s)
ω = angular speed (radians/s)
r = radius of the rotation (m)
------------
Given:
d= 44 cm ⇒ r= 44/2 cm= 22 cmω= 4 rev/0.5 s= 8 rev/s= 8*2π/s= 16π/s (converted rev to radians)Linear speed is:
v= 22*16π cm/s ≈ 1106 cm/s (rounded to full number)Each of 100 students in the Allen School can only take 1 CSE class each, between the four classes CSE 311, CSE 312, CSE 331, and CSE 332. Each student (independently of others) takes CSE 311 with probability 0.3, CSE 312 with probability 0.4, CSE 331 with probability 0.1, and CSE 332 with probability 0.2. What is the probability that exactly 31 sign up for CSE 311, 39 sign up for CSE 312, 7 sign up for CSE 331, and 23 sign up for CSE 332
Answers
Answer:
[tex]P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
Step-by-step explanation:
Sample space, n = 100
Let the number of students signed up for CSE 311 = a
Let the number of students signed up for CSE 312 = b
Let the number of students signed up for CSE 331 = c
Let the number of students signed up for CSE 332 = d
Probability of taking CSE 311, [tex]P_a[/tex] = 0.3
Probability of taking CSE 312, [tex]P_b[/tex] = 0.4
Probability of taking CSE 331, [tex]P_c[/tex] = 0.1
Probability of taking CSE 332, [tex]P_d[/tex] = 0.2
[tex]P(a,b,c,d) = \frac{n!}{a! b! c! d!} p_a^{a} p_b^{b} p_c^{c} p_d^{d} \\P(a=31,b=39,c=7,d=23) = \frac{100!}{31! 39! 7! 23!} * 0.3^{31} * 0.4^{39} * 0.1^{7} 0.2^{23}\\P(a=31,b=39,c=7,d=23) = \frac{4.58*10^{111}}{2.13*10^{56}* 5040 }* (1.57*10^{-55})\\P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
PLEASE HELPP! f(x)= -3x + 3
Which of the graphs represent the inverse of the function F??
Answers
Answer:
Answer is Y
Step-by-step explanation:
What are the characteristics of a socialist economy? What are the pros and cons of this type of economy?
Answers
Answer:
The pro is Political Control, the cons, however, are many.
Step-by-step explanation:
However, A Socialist Economy cons outweigh its pros. The only thing that is a PRO is you dictating it, preventing people from success. Wanna know the cons? The Cons are more Regulations, to which chokes more businesses of their money, they function, & motive. To which it has a chain reaction of: The Businesses not employing people, more people are out of work, which means more people ain't buying stuff to support the businesses, which means the businesses are out of business, they shut down.
The Economy ain't something that you can stop, or go, & it ain't statistics. An Economy is just.. people, that's it. It's just people, they are the ones that work, run businesses & factories, they are the ones that buy N' sell. They create, craft, invent, innovate, etc.
Here's a quote that I have: "The more you choke it from breathing in, the less it breathes out". That's my stance on regulation & Socialism, to which Socialism is just Voluntary Communism, & A Permanent Ideological belief that Big government Involvement is the way to go.
To which, it's not!
Describe fully the single transformation that’s maps triangle A onto triangle B.
Answers
Answer:
reflection of the axis y=4
Step-by-step explanation:
becuase it is reflected on itself
Answer:
Reflect Triangle A by the line y = 4
Step-by-step explanation:
The answer is reflect Triangle A by y = 4 because the two triangles are symmetric.
Stuck on this one .......
Answers
Answer:
Exponent Product Rule
Step-by-step explanation:
Exponent multiplication: (a^b)(a^c)= a^(b+c)
t^3=(t^2)t
Because t=t^1, we have
t^2+t^1=t^3
This can be shown by the Exponent Product Rule
Answer: t²⁺¹
Step-by-step explanation:
The law of exponents states that when multiplying terms with the same base, you ADD the exponents. Note that "t" has an exponent of 1.
t³ = (t²)t¹ = t²⁺¹
I hope this is what you were looking for.
For the data set represented by this box plot, what is the value of the maximum? maximum:
Answers
Answer:
140
Step-by-step explanation:
The maximum is the furthest the line that goes out the furthest, the minimum would be about 83-84
Answer:
the other person is correct!
Step-by-step explanation:
Kajol has $75. This is 3/8 of the amount she earned. How much did she earn?
Answers
Answer:
$200
I hope this helps!
Answer:
200rupees
Step-by-step explanation:
according to the question ,kajol has 75 rupees
amount earned=3/8* amount earned
=75/3*8
=200 rupees
The half-life of a radioactive substance is one day, meaning that every day half of the substance has decayed. Suppose you have 95 grams of this substance. Construct an exponential model for the amount of the substance remaining on a given day. Use your model to determine how much of the substance will be left after 4 days
Answers
Answer:
Exponential model
Y = y0e-0.693(t½)
Amount remaining after 4 days
5.9413 grams
Step-by-step explanation:
The formula will he given by
Y = y0e-k(t½)
The half life t½ for this radioactive substance is a day.
Initial mass y0 = 95 grams
Mass after one day = 95/2
Mass after one day = 47.5
.
Value of the decay constant k is not given, let's look for k.
Y = y0e-k(t½)
47.5= 95e-k(1)
47.5/95= e-k(1)
0.5= e-k(1)
In 0.5 = -k
-0.693= -k
0.693 = k
Y = y0e-0.693(t½)
Amount remaining after 4 days
Y = y0e-0.693(t½)
Y = 95e-0.693(4)
Y= 95e-2.772
Y= 95(0.06254)
Y= 5.9413 grams
How much time will it take Jenny to bike 15 miles if she bikes at a speed of 6 mph?
Answers
Answer:
this lesson, we will investigate the relationship between the distance traveled, the rate or speed or travel, and the time that it takes to travel that distance at that rate. We will also look at a few other related products.
Distance = (Rate)(Time)
The equation that relates distance, rate, and time is
d = rt
Where d is the distance traveled, r is the rate, and t is the time. On the CAHSEE exam, you will be given two of these and will be asked to use the above equation to find
took Markus half an hour to drive home from work. He averaged 34 miles per hour. How far does Markus live from his work?SolutionWe are given that it takes 1/2 an hour for the trip. This is a time: t = 1/2We are given that he averages 34 miles per hour. This is a rate: r = 34We are asked how few he has traveled. This is a distance. We use the d=rt equation: d = rt = (34)(1/2) = 17Answer:
2.5 hours
Step-by-step explanation:
First, try rewriting Jenny's speed in it's fraction form: 6 mi/hr
Next, use the units to set up an equation that relates Jenny's speed to the distance they want to travel. Let's call the unknown time t:
6mi/hr=15mi/t
1/t=6/15 (mi/hr•1/mi)
t=15/6 (hrs/mi•mi)= 15/6 (hrs•mi/mi)= 15/6 hrs
t=2.5hrs
So it'd take Jenny 2.5hrs at 6mph to go 15 miles. The key here is to keep track of the units. You can treat them like fractions and reduce them away as if they were numbers or variables.